The pontiff, speaking to the French Catholic daily La Croix, said that a resignation of Cardinal Philippe Barbarin "would be a mistake, an imprudence".
He went on: "Based on the information I have, I think in Lyon, Cardinal Barbarin has taken the necessary measures and has taken things well in hand.
"He is a brave and creative man, a missionary."
Francis said "we must now wait for the result of the proceedings before the civil courts", but resigning now "would amount to admitting guilt".
The cardinal is one of the most high-ranking officials in the French Catholic Church and is involved in two investigations for not reporting cases of child abuses by priests to judicial authorities.
He has denied any cover-ups, but admitted "some mistakes in handling and appointing some priests" last month.
Other church officials have been also investigated.
Speaking to La Croix, Pope Francis also said that in allegations of paedophile priests in general, for the church, "there can be no prescription" and that "tolerance must be zero".
He continued: "Through these abuses, a priest, who is designed to drive a child to God, is destroying him. He spreads evil, resentment, pain."
Francis gave the special 60 minute interview in his Vatican home earlier in May.
